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The Entrance Laws of Self-Similar Markov Processes and Exponential Functionals of Lévy Processes

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Abstract

We consider the asymptotic behavior of semi-stable Markov processes valued in ]0,∞[ when the starting point tends to 0. The entrance distribution is expressed in terms of the exponential functional of the underlying Lévy process which appears in Lamperti's representation of a semi-stable Markov process.

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Bertoin, J., Yor, M. The Entrance Laws of Self-Similar Markov Processes and Exponential Functionals of Lévy Processes. Potential Analysis 17, 389–400 (2002). https://doi.org/10.1023/A:1016377720516

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